"This isn't about censorship or restricting freedom, it's simply about protecting children whilst allowing adults to do as they choose within the law," said Peter Wanless, chief executive officer of the National Society for the Prevention of Cruelty to Children.
Cameron said it was not entirely clear how the measures would work, but service providers should be able to come up with solutions.
"If there are technical obstacles to acting on this, don't just stand by and say nothing can be done; use your great brains to overcome them," he said.
"You're the people who have worked out how to map almost every inch of the earth from space, who have algorithms that make sense of vast quantities of information. You're the people who take pride in doing what they say can't be done."
But Padraig Reidy of free-speech group Index on Censorship said the proposals amounted to "a kind of default censorship."
"If a filter is set up as a default then it can really restrict what people can see legitimately," he told BBC radio. "Sites about sexual health, about sexuality and so on, will get caught up in the same filters as pornography. It will really restrict people's experience on the web, including children's."
Columnist Nick Cohen, of the Spectator magazine, said recent disclosures about government snooping should make people wary of giving companies and authorities personal information such as a desire to view pornography.
"The expansion of legislation prohibiting pornographic images may sound equally reasonable until you remember it gives more powers to police and prosecutors," he wrote. "The record shows they cannot be trusted to use them justly."
